Non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor instability using the macroscopic forcing method

Abstract

The importance of non-locality of mean scalar transport in two-dimensional Rayleigh–Taylor Instability (RTI) is investigated. The macroscopic forcing method is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about non-locality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient to capture the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers–Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.